Simulations of wave propagation in the Earth usually require truncation of a larger domain to the region of interest to keep computational cost acceptable. This introduces artificial boundaries that should not generate reflected waves. Most existing boundary conditions are not able to completely suppress all the reflected energy, but suffice in practice except when modelling subtle events such as interbed multiples. Exact boundary conditions promise better performance but are usually formulated in terms of the governing wave equation and, after discretization, still may produce unwanted artefacts. Numerically exact non‐reflecting boundary conditions are instead formulated in terms of the discretized wave equation. They have the property that the numerical solution computed on a given domain is the same as one on a domain enlarged to the extent that waves reflected from the boundary do not have the time to reach the original truncated domain. With a second‐ or higher‐order finite‐difference scheme for the one‐dimensional wave equation, these boundary conditions follow from a recurrence relation. In its generalization to two or three dimensions, a recurrence relation was only found for a single non‐reflecting boundary on one side of the domain or two of them at opposing ends. The other boundaries should then be zero Dirichlet or Neumann. If two non‐reflecting boundaries meet at a corner, translation invariance is lost and a simple recurrence relation could not be found.

中文翻译：

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研究注：在数值精确的非反射边界条件下拐角问题的解决方法

模拟地球中的波传播通常需要将较大的域截断到感兴趣的区域，以使计算成本保持可接受的水平。这引入了不应产生反射波的人工边界。大多数现有的边界条件不能完全抑制所有反射能量，但是在实际中就足够了，除非对微妙的事件（例如互穿倍数）进行建模。精确的边界条件有望带来更好的性能，但通常是根据控制波动方程制定的，离散化之后，仍然可能会产生不需要的伪像。取而代之的是，根据离散波方程来公式化数字精确的非反射边界条件。它们具有以下特性：在给定域上计算出的数值解与在扩展到一定程度的域上的解（从边界反射的波没有时间到达原始截断域）相同。对于一维波动方程，采用二阶或更高阶有限差分方案时，这些边界条件遵循递归关系。在将其推广到二维或三维时，仅在域的一侧或两个相对端发现了一个非反射边界的递归关系。则其他边界应为零Dirichlet或Neumann。如果两个非反射边界在拐角处相遇，则平移不变性将丢失，并且无法找到简单的递归关系。